\[ \int \frac {-540+e^2 (45-9 x)-81 x+81 x^2+(108-27 x) \log (5)}{-3375 x^3-2025 x^4-405 x^5-27 x^6+e^6 \left (1+3 x+3 x^2+x^3\right )+e^4 \left (-45 x-99 x^2-63 x^3-9 x^4\right )+e^2 \left (675 x^2+945 x^3+297 x^4+27 x^5\right )+\left (2025 x^3+810 x^4+81 x^5+e^4 \left (9 x+18 x^2+9 x^3\right )+e^2 \left (-270 x^2-324 x^3-54 x^4\right )\right ) \log (5)+\left (-405 x^3-81 x^4+e^2 \left (27 x^2+27 x^3\right )\right ) \log ^2(5)+27 x^3 \log ^3(5)} \, dx \]
Optimal antiderivative \[ \frac {-2+x}{x^{2} \left (x -\ln \left (5\right )+\frac {\left (-\frac {1}{3}-\frac {x}{3}\right ) {\mathrm e}^{2}}{x}+5\right )^{2}} \]
command
integrate(((-27*x+108)*log(5)+(-9*x+45)*exp(2)+81*x^2-81*x-540)/(27*x^3*log(5)^3+((27*x^3+27*x^2)*exp(2)-81*x^4-405*x^3)*log(5)^2+((9*x^3+18*x^2+9*x)*exp(2)^2+(-54*x^4-324*x^3-270*x^2)*exp(2)+81*x^5+810*x^4+2025*x^3)*log(5)+(x^3+3*x^2+3*x+1)*exp(2)^3+(-9*x^4-63*x^3-99*x^2-45*x)*exp(2)^2+(27*x^5+297*x^4+945*x^3+675*x^2)*exp(2)-27*x^6-405*x^5-2025*x^4-3375*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {9 \, {\left (x - 2\right )}}{{\left (3 \, x^{2} - x e^{2} - 3 \, x \log \left (5\right ) + 15 \, x - e^{2}\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________